Efficient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT: Experimental Evaluation

For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1-ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we consider r-BLOCKINip neighborhoods for r = 2; 3, and examine their eectiveness by computational experiments. In the accompanying paper, we proposed new implementations of these neighborhoods, and showed that the expected size of 2-BLOCKINip neighborhood is O(n +m) and that of 3-BLOCKINip neighborhood is O(m + t 2 n), compared to their original size O(n 2) and O(n 3), respectively, where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. These are used in this paper under the framework of tabu search and other metaheuristic methods, and compared with other existing algorithms with 1-BLOCKINip neighborhood. The results exhibit good prospects of larger neighborhoods.